I always explained it to myself that the eng/sci teams had to take turns lining up to use the transporter room, since the various Team abilities fall under Crew systems and it even makes the transporter sound when you use one. It's like the science team is beaming to the area on your ally's/your own ship that's in trouble.

Of course, my explanation doesn't cover how the problem's fixed as soon as they beam over, or that they can beam through shields during battle, but after all, it's just a game.